Partial stability analysis of some classes of nonlinear systems

Alexander ALEKSANDROV, Elena ALEKSANDROVA, Alexey ZHABKO, Yangzhou CHEN

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A nonlinear differential equation system with nonlinearities of a sector type is studied. Using the Lyapunov direct method and the comparison method, conditions are derived under which the zero solution of the system is stable with respect to all variables and asymptotically stable with respect to a part of variables. Moreover, the impact of nonstationary perturbations with zero mean values on the stability of the zero solution is investigated. In addition, the corresponding time-delay system is considered for which delay-independent partial asymptotic stability conditions are found. Three examples are presented to demonstrate effectiveness of the obtained results.

Original languageEnglish
Pages (from-to)329-341
Number of pages13
JournalActa Mathematica Scientia
Volume37
Issue number2
DOIs
StatePublished - 1 Mar 2017

Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

Keywords

  • Lyapunov function
  • Nonlinear systems
  • partial asymptotic stability
  • sector nonlinearities
  • time-delay

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